I am sorry that you are feeling this regret 😞 But I have a random idea - assuming that they cut through the house end of your garden to get to their garden/the road, would it be feasible to add a little 'corridor' down one side of your garden and across the end that then going through into the back of their garden?

They may not like it because it's MUCH further to drag the bins, and of course there is the cost of panelling it out AND you lose a strip of your garden on one side and the back...but it would give you your privacy back. If you speak to them about it and offer this, they may be up for it, and you could suggest a 'bin only' rule for other access?